I don't think they would have too many problems, mostly because they both have little tolerance for idiots and such, but I would imagine Rush would be a bit resentful of McKay.I wonder how much McKay will piss off Rush...it shouldn't take that long for some friction between them to happen.
People who have similar personality types don't always get along with each other. I think if they got in the same room with each other they just might clash especially with their egos as big as they are. They might thin the other isn't as smart as they are.
They ought to have Rodney switch bodies with her:
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